There are two things that affect DoF in a big way - your aperture, and distances.
To put it simply, the more open your aperture, the more shallow the DoF. That's one of the reasons landscape photographers use a small aperture - they want their DoF to be as wide as possible so they can capture a large range of scenery in focus.
As for distances, I'll once again simplify (perhaps oversimplification in this case). Put your subject close to your lens, and keep the background far away. If you're not getting the desired result, pull your subject further away from the background.
Take a look at
this blog post, as well as the rest of the beginner's tips. Also, follow along with the 101 posts. The next post is slated to be on aperture, which is bound to have some material on Depth of Field.